高数积分.ln{x^1/2 + (1+x)^1/2}dx.请写出详细步骤,谢谢.
问题描述:
高数积分.ln{x^1/2 + (1+x)^1/2}dx.请写出详细步骤,谢谢.
答
用分部积分法.∫ln{x^1/2 + (1+x)^1/2}dx=xln{x^1/2 + (1+x)^1/2}-∫xdln{x^1/2 + (1+x)^1/2}=xln{x^1/2 + (1+x)^1/2}-1/2∫x/√(x(x+1) dx=xln{x^1/2 + (1+x)^1/2}-1/2√(x(x+1)+1/4ln│x+1/2+√(x(x+1)│+C...